An interesting study might be parents who later learn that their kids aren't actually theirs. Did they treat their kids differently than real biological children? All kinds of ethical issues, etc., but the data would be awesome.
We can assume that nobody treats them better and some will treat them worse. It follows that non-biological parents inevitably treat on average (and, very important, this is cross-sectional, not paired) their kids worse after they know they are not theirs. Directionally, there is little doubt.
Even if you could resolve the ethical issues, the only thing that a study would prove is that “people tend not to care for children that aren’t theirs”, and not “biological relation is necessary for a parent to be able to care for an adopted child”.
No I meant how people treated those kids before they learned that the kids weren't theirs.